@article{703,
abstract = {We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some labels of the considered graphical model either as (i) optimal, meaning that they belong to all optimal solutions of the inference problem; (ii) non-optimal if they provably do not belong to any solution. With access to an exact solver of a linear programming relaxation to the MAP-inference problem, our algorithm marks the maximal possible (in a specified sense) number of labels. We also present a version of the algorithm, which has access to a suboptimal dual solver only and still can ensure the (non-)optimality for the marked labels, although the overall number of the marked labels may decrease. We propose an efficient implementation, which runs in time comparable to a single run of a suboptimal dual solver. Our method is well-scalable and shows state-of-the-art results on computational benchmarks from machine learning and computer vision.},
author = {Shekhovtsov, Alexander and Swoboda, Paul and Savchynskyy, Bogdan},
issn = {01628828},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
number = {7},
pages = {1668--1682},
publisher = {IEEE},
title = {{Maximum persistency via iterative relaxed inference with graphical models}},
doi = {10.1109/TPAMI.2017.2730884},
volume = {40},
year = {2018},
}
@inproceedings{274,
abstract = {We consider the problem of estimating the partition function Z(β)=∑xexp(−β(H(x)) of a Gibbs distribution with a Hamilton H(⋅), or more precisely the logarithm of the ratio q=lnZ(0)/Z(β). It has been recently shown how to approximate q with high probability assuming the existence of an oracle that produces samples from the Gibbs distribution for a given parameter value in [0,β]. The current best known approach due to Huber [9] uses O(qlnn⋅[lnq+lnlnn+ε−2]) oracle calls on average where ε is the desired accuracy of approximation and H(⋅) is assumed to lie in {0}∪[1,n]. We improve the complexity to O(qlnn⋅ε−2) oracle calls. We also show that the same complexity can be achieved if exact oracles are replaced with approximate sampling oracles that are within O(ε2qlnn) variation distance from exact oracles. Finally, we prove a lower bound of Ω(q⋅ε−2) oracle calls under a natural model of computation.},
author = {Kolmogorov, Vladimir},
booktitle = {Proceedings of the 31st Conference On Learning Theory},
pages = {228--249},
publisher = {PMLR},
title = {{A faster approximation algorithm for the Gibbs partition function}},
volume = {75},
year = {2017},
}
@misc{5561,
abstract = {Graph matching problems as described in "Active Graph Matching for Automatic Joint Segmentation and Annotation of C. Elegans." by Kainmueller, Dagmar and Jug, Florian and Rother, Carsten and Myers, Gene, MICCAI 2014. Problems are in OpenGM2 hdf5 format (see http://hciweb2.iwr.uni-heidelberg.de/opengm/) and a custom text format used by the feature matching solver described in "Feature Correspondence via Graph Matching: Models and Global Optimization." by Lorenzo Torresani, Vladimir Kolmogorov and Carsten Rother, ECCV 2008, code at http://pub.ist.ac.at/~vnk/software/GraphMatching-v1.02.src.zip. },
author = {Kainmueller, Dagmar and Jug, Florian and Rother, Carsten and Meyers, Gene},
keywords = {graph matching, feature matching, QAP, MAP-inference},
publisher = {IST Austria},
title = {{Graph matching problems for annotating C. Elegans}},
doi = {10.15479/AT:ISTA:57},
year = {2017},
}
@inproceedings{641,
abstract = {We introduce two novel methods for learning parameters of graphical models for image labelling. The following two tasks underline both methods: (i) perturb model parameters based on given features and ground truth labelings, so as to exactly reproduce these labelings as optima of the local polytope relaxation of the labelling problem; (ii) train a predictor for the perturbed model parameters so that improved model parameters can be applied to the labelling of novel data. Our first method implements task (i) by inverse linear programming and task (ii) using a regressor e.g. a Gaussian process. Our second approach simultaneously solves tasks (i) and (ii) in a joint manner, while being restricted to linearly parameterised predictors. Experiments demonstrate the merits of both approaches.},
author = {Trajkovska, Vera and Swoboda, Paul and Åström, Freddie and Petra, Stefanie},
editor = {Lauze, François and Dong, Yiqiu and Bjorholm Dahl, Anders},
isbn = {978-331958770-7},
location = {Kolding, Denmark},
pages = {323 -- 334},
publisher = {Springer},
title = {{Graphical model parameter learning by inverse linear programming}},
doi = {10.1007/978-3-319-58771-4_26},
volume = {10302},
year = {2017},
}
@article{644,
abstract = {An instance of the valued constraint satisfaction problem (VCSP) is given by a finite set of variables, a finite domain of labels, and a sum of functions, each function depending on a subset of the variables. Each function can take finite values specifying costs of assignments of labels to its variables or the infinite value, which indicates an infeasible assignment. The goal is to find an assignment of labels to the variables that minimizes the sum. We study, assuming that P 6= NP, how the complexity of this very general problem depends on the set of functions allowed in the instances, the so-called constraint language. The case when all allowed functions take values in f0;1g corresponds to ordinary CSPs, where one deals only with the feasibility issue, and there is no optimization. This case is the subject of the algebraic CSP dichotomy conjecture predicting for which constraint languages CSPs are tractable (i.e., solvable in polynomial time) and for which they are NP-hard. The case when all allowed functions take only finite values corresponds to a finitevalued CSP, where the feasibility aspect is trivial and one deals only with the optimization issue. The complexity of finite-valued CSPs was fully classified by Thapper and Živný. An algebraic necessary condition for tractability of a general-valued CSP with a fixed constraint language was recently given by Kozik and Ochremiak. As our main result, we prove that if a constraint language satisfies this algebraic necessary condition, and the feasibility CSP (i.e., the problem of deciding whether a given instance has a feasible solution) corresponding to the VCSP with this language is tractable, then the VCSP is tractable. The algorithm is a simple combination of the assumed algorithm for the feasibility CSP and the standard LP relaxation. As a corollary, we obtain that a dichotomy for ordinary CSPs would imply a dichotomy for general-valued CSPs.},
author = {Kolmogorov, Vladimir and Krokhin, Andrei and Rolinek, Michal},
journal = {SIAM Journal on Computing},
number = {3},
pages = {1087 -- 1110},
publisher = {SIAM},
title = {{The complexity of general-valued CSPs}},
doi = {10.1137/16M1091836},
volume = {46},
year = {2017},
}